Matlab绘制剪切力和弯曲矩图

%% Shear Force & Bending Moment Examples

%     This program calculates the shear force and bending moment profiles, 
%     draws the free body, shear force and bending moment diagrams of the 
%     problem.
% 
%     Under the free body diagram, the equations of each section is clearly 
%     written with Latex
% 
%% How to call the function
%     To use this program, you need to call the solve function on the instance 
%     of the SFBMProb object that has the complete problem description.
%     You first create the SFBMProb Object and then add the loads in no
%     partcular order. 
% 
%% How to create the SFBMProb object
%     create an instance of SFBMProb by calling "SFBMProb" with three
%     arguments. The first is the name of the problem. For instance, 
%     "Example 1", the second argument is Length of the beam, and the third
%     is locations of the supports. 
%
%     prob = SFBMProb(name, length, supports)
%%-   Cantilever
%       If the problem is a cantilever problem, then you have only one clamped 
%       support, at the beginning or end of the beam. In such a case, the number is
%       second argument contains 2 elements instead of three. 
%
%       For instance, for a cantilever of length 20m, supported at the beginning, 
%       prob = SFBMProb("Cantilever", 20, 0)
%       and if supported at the end, 
%       prob = SFBMProb("Cantilever", 20, 20)

%%-   Beam on the floor
%       Its possible to have a problem in which the body is lying on the floor 
%       without any point support. In such scenario, 
%       prob = SFBMProb("BeamOnFloor", 20, [])
%
%% Set Units
%     We have just two primary physical quantities here: Force and Legnth.
%     ForceUnit default is KN
%     LengthUnit default is m

%     but to set a preferred unit, use
%
%     prob.ForceUnit = "lb";
%     prob.LengthUnit = "inch";

%% Load Description
%     Loads can be Force: such point or distributed load, or Torque the we
%     call Moment here. In general Load would have value and location.
%     The sign of the value can indicate whether it is pointing upwards, or
%     downwards in the case of force, or clockwise/anticlockwise in case of
%     moment. While moment and point load have scalars for value and
%     location, distributed load have vector of value and location. 

%% How to add loads to the object.
%
%%-   Moment(Torque)
%         To add a clockwise moment of magnitude 3KN-m applied at point 5m
%         prob.AddMomentLoad(-3, 5);
%         For an anticlockwise moment of magnitude 7KN-m applied at point 8m
%         prob.AddMomentLoad(7, 8);
%
%%-   Concentrated Load(Force)
%         To add a downward point load of magnitude 0.8KN applied at point 3m
%         prob.AddPointLoad(-0.8, 3);
%         For an upward point load of magnitude 5KN-m applied at point 7m
%         prob.AddMomentLoad(5, 7);
%
%%-   Distributed Force
%         To add uniform upward distributed load of magnitude 2KN/m applied from point 3 to 5m 
%         prob.AddDistLoad([2, 2], [3, 5]);
%         For linearly increasing distributed load 2KN/m  to 5KN/m applied from point 3 to 5m 
%         prob.AddDistLoad([2, 5], [3, 5]);


%%     Example(1)

%Problem Name
Name = 'Example 1';

%Length and Supports
Length = 10; Supports = [2, 10]; % length  = 10, supports at 2 and 10;
prob = SFBMProb(Name, Length, Supports);

%Set Unit
prob.ForceUnit = 'lb';
prob.LengthUnit = 'inch';

%Concetrated Loads
prob.AddPointLoad(-5, 0); % 5N downward at point 0
prob.AddPointLoad(-10, 8); % 10N downward at point 8

%Torques
prob.AddMoment(10, 3);  % ACW 10Nm at point 3
prob.AddMoment(-10, 7); % CW 10Nm at point 7

%Solve the problem
prob.Solve()

%%     Example(2)
%Problem Name
Name = 'Example 2';

%Length and Supports
Length = 20; Supports = 0; % length  = 20m, Cantilever supported at 0 m;
prob = SFBMProb(Name, Length, Supports);

%Concentrated Loads
prob.AddPointLoad(-5, 6);   % 5N downward at point 6
prob.AddPointLoad(-10, 13); % 10N downward at point 13

%Distributed Loads
prob.AddDistLoad([5,5],[1,3]);    % Constant 5N/m upwards from 1m to 3 m 
prob.AddDistLoad([-4,-4],[14,17]); % Constant 4N/m downwards from 14m to 17 m

%Solve the problem
prob.Solve()

%%     Example(3)
%Problem Name
Name = 'Example 3';
% Length and Supports
Length = 30; Supports = [0,20]; % length  = 30m, supports at 0m and 20m;
prob = SFBMProb(Name, Length, Supports);

% Concentrated Loads
prob.AddPointLoad(-20, 6);   % 20N downward at point 6
prob.AddPointLoad(-10, 13);  % 10N downward at point 13
prob.AddPointLoad(5, 27);    % 5N upward at point 27

% Torques
prob.AddMoment(50, 8);  % ACW 50Nm at point 8
prob.AddMoment(-45, 25); % CW 45Nm at point 25

% Distributed Loads
prob.AddDistLoad([7, 7], [1,3]);    % Constant 7N/m upwards from 1m to 3m 
prob.AddDistLoad([-5,-5], [12,18]); % Constant 5N/m downwards from 12m to 18m

% Solve the problem
prob.Solve()

%%     Example(4)
%Problem Name
Name = 'Example 4';
% Length and Supports
Length = 20; Supports = [5,20]; % length  = 20m, supports at 5m and 20m;
prob = SFBMProb(Name, Length, Supports);

% Concentrated Loads
prob.AddPointLoad(-2, 0);   % 2N downward at point 0

% Torques
prob.AddMoment(50, 8);  % ACW 50Nm at point 8
prob.AddMoment(-45, 15); % CW 45Nm at point 15

% Distributed Loads
prob.AddDistLoad([5, 5], [1,3]);    % Constant 7N/m upwards from 1m to 3m 
prob.AddDistLoad([-4, -4], [14, 17]); % Constant 5N/m downwards from 12m to 18m

% Solve the problem
prob.Solve()

%%     Example(4)
%Problem Name
Name = 'Example 4';
% Length and Supports
Length = 20; Supports = [6,20]; % length  = 20m, supports at 5m and 20m;
prob = SFBMProb(Name, Length, Supports);

% Concetrated Loads
prob.AddPointLoad(-2,0);  % 2N downward at point 0

% Torques
prob.AddMoment(10,8);   % ACW 10Nm at point 8
prob.AddMoment(-15,12); % CW 10Nm at point 12

% Distributed Loads
prob.AddDistLoad([5, 2, 5], [1, 3, 5]);    % Quadratic profile distributed upwards force from 1m to 5m and 
prob.AddDistLoad([-4, -2, -4],[14, 16, 18]); % Quadratic profile distributed downwards force from 14m to 18m

% Solve the problem
prob.Solve()


%%     Example(5)
%Problem Name
Name = 'Example 5';
% Length and Supports
Length = 20; Supports = [6,20]; % length  = 20m, supports at 5m and 20m;
prob = SFBMProb(Name, Length, Supports);

% Concetrated Loads
prob.AddPointLoad(-2,0);  % 2N downward at point 0

% Torques
prob.AddMoment(10,8);   % ACW 10Nm at point 8
prob.AddMoment(-15,12); % CW 10Nm at point 12

% Distributed Loads
prob.AddDistLoad([5, 2], [1, 3]);    % Linear profile upwards from 1m to 3m and 
prob.AddDistLoad([2, 5], [3, 5]);    % Linear profile upwards from 3m to 5m and 
prob.AddDistLoad([-4, -2],[14, 16]); % Linear profile downwards from 14m to 16m
prob.AddDistLoad([-2, -4],[16, 18]); % Linear profile downwards from 16m to 18m

% Solve the problem
prob.Solve()

%%     Example(6)
%Problem Name
Name = 'Wikipedia';
Length = 50; Supports = 50;
prob = SFBMProb(Name, Length, Supports);
prob.Source = "https://en.wikipedia.org/wiki/Shear_and_moment_diagram#Calculating_shear_force_and_bending_moment";

%Set Units
prob.ForceUnit = 'k';
prob.LengthUnit = 'ft';

% Concetrated Loads
prob.AddPointLoad(-10,0); 
prob.AddPointLoad(25.3,10); 
prob.AddPointLoad(-3.5,25); 

% Torques
prob.AddMoment(-50,37.5); 

% Distributed Loads
prob.AddDistLoad([-1,-1], [10,25]);  

% Solve the problem
prob.Solve()